This is a grant application for methodological research in statistical issues related to community-based studies in cancer and environment. The proposed activities are motivated by the projects of cancer prevention and environmental epidemiology that the PI is currently involved in. Specifically, the PI plans to: (1) Establish models for spatial survival data. We propose two classes of models: spatial frailty survival models and marginal spatial survival models. We develop the imputed partial likelihood score method to draw inference based on the frailty models. For the marginal survival models, we adapt the composite likelihood approach and develop an estimating equation to estimate the regression coefficients and the variance components simultaneously. (2) Study two special aspects of spatial survival data. We analyze spatial failure time data with general censoring types, including right, left and interval censoring. We develop models for spatially correlated failure time data with measurement errors in covariates. (3) Develop models for spatially correlated data that are observed in discrete time (for example, at regular, pre-specified follow-up times). Specifically, we consider models for spatially correlated grouped survival data and spatial transitional regression models for the analysis of repeated discrete responses, e.g. binary status, observed in a spatial setting. To cope with informative or non-ignorable dropout, we also propose jointly modeling the grouped survival and the transitional processes. Empirical data analysis will play a central role in all specific aims. Available relevant data include Workers Against Risk of Tobacco Study, East Boston Asthma Study and Established Populations for the Epidemiologic Study of the Elderly. Although motivated by applied problems in cancer and environmental health studies, the proposed research offers useful contributions to general statistical methodology in survival analysis, spatial analysis, longitudinal data analysis and measurement error modeling.